She said she had been overwhelmed by the response she had received so far.

"I used to work as an estate agent in Chiswick and I often saw her around," Ms Daniels, who lives in Acton, told getwestlondon. "When her car was removed by the council she didn't seek any help.

"She was an independent lady and I admired that.

"She lived out in the freezing cold, never accepting any charity, and then she got hit by a truck. She didn't deserve to die like that.

"I recently attended a funeral for an old family friend at which only four people turned up. Annie was a local legend and I thought she doesn't deserve to be sent off alone.

"I've been so touched by all the messages, which show how well admired she was."

Police have so far been unable to contact any relatives of Ms Naysmith, who became a local celebrity after sleeping in her car and later on the streets after losing her home in Prebend Gardens in the '70s.

Hounslow Council is arranging Ms Naysmith's funeral and several churches she used to attend have expressed an interest in hosting the service, including St Michael and All Angels, in Bedford Park.

Well-wishers have been laying flowers and lit candles at Ms Naysmith's old shelter, beside the car park round the back of Stamford Brook tube station, at the end of Welstead Way, but Ms Daniels would like to see a more lasting memorial like a tree or bench near to the spot.

She has also called on local shopkeepers to place a red rose in their windows as a mark of respect and is considering starting a memorial appeal to raise money in Ms Naysmith's name for Youth Music, the charity supported by the family of tragic teenager Alice Gross.

Council leader Steve Curran has joined those paying their respects and said details of Ms Naysmith's funeral would be announced as soon as possible.

He added: "We are incredibly saddened by the news of the death of Anne Naysmith in the early hours of February 10 2015 and understand how popular she was with the local community in Chiswick.

"Our deepest condolences are with those who knew Anne. She was a real character who will be fondly remembered by many."